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A111855 Number of numbers m <= n such that 5 equals the first digit after decimal point of square root of n in decimal representation. 11

%I

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,

%T 2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,

%U 4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7

%N Number of numbers m <= n such that 5 equals the first digit after decimal point of square root of n in decimal representation.

%C For n > 1: if A023961(n)=5 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).

%C Lim_{n->infinity} a(n)/n = 1/10.

%D G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.

%e a(10) = 0, a(100) = 7, a(1000) = 93, a(10000) = 970.

%Y Cf. A111850, A111851, A111852, A111853, A111854, A111856, A111857, A111858, A111859, A111895.

%K nonn,base

%O 1,31

%A _Reinhard Zumkeller_, Aug 20 2005

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Last modified March 2 09:45 EST 2021. Contains 341746 sequences. (Running on oeis4.)